Hierarchical predictive coding (hPC) proposes that the cortex continuously generates predictions of incoming sensory stimuli. Deep neural networks inspired by hPC are frequently used to probe the neurocomputational mechanisms suggested by the theory in silico and to generate hypotheses for experimental investigations. However, these networks often deviate from hPC by prioritizing computational efficiency over alignment with its principles. To remedy this, we introduce PrediRep, a deep learning model explicitly designed to emphasize alignment with the theory. PrediRep incorporates the principles of hPC found in the other networks, while avoiding their deviations from it. We evaluate the performance of PrediRep on a next-frame prediction task and its functional alignment with hPC, comparing it to other contemporary deep learning networks inspired by the theory. Our findings demonstrate that PrediRep achieves the closest functional alignment with hierarchical predictive coding without sacrificing computational performance.